Reduced-Order Surrogates for Forced Flexible Mesh Coastal-Ocean Models
This work addresses the need for efficient and reliable surrogate models for coastal-ocean modelling, enabling ensemble forecasting and long climate simulations, though it is incremental as it builds on existing Koopman and POD methods.
This paper tackled the problem of developing accurate and stable reduced-order surrogates for forced flexible mesh coastal-ocean models, introducing a Koopman autoencoder that outperformed POD-based surrogates with relative root-mean-squared-errors of 0.01-0.13 and R²-values of 0.65-0.996 across test cases, achieving inference speed-ups of 300-1400x.
While POD-based surrogates are widely explored for hydrodynamic applications, the use of Koopman Autoencoders for real-world coastal-ocean modelling remains relatively limited. This paper introduces a flexible Koopman autoencoder formulation that incorporates meteorological forcings and boundary conditions, and systematically compares its performance against POD-based surrogates. The Koopman autoencoder employs a learned linear temporal operator in latent space, enabling eigenvalue regularization to promote temporal stability. This strategy is evaluated alongside temporal unrolling techniques for achieving stable and accurate long-term predictions. The models are assessed on three test cases spanning distinct dynamical regimes, with prediction horizons up to one year at 30-minute temporal resolution. Across all cases, the Koopman autoencoder with temporal unrolling yields the best overall accuracy compared to the POD-based surrogates, achieving relative root-mean-squared-errors of 0.01-0.13 and $R^2$-values of 0.65-0.996. Prediction errors are largest for current velocities, and smallest for water surface elevations. Comparing to in-situ observations, the surrogate yields -0.65% to 12% change in water surface elevation prediction error when compared to prediction errors of the physics-based model. These error levels, corresponding to a few centimeters, are acceptable for many practical applications, while inference speed-ups of 300-1400x enables workflows such as ensemble forecasting and long climate simulations for coastal-ocean modelling.